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LUKHDHIRJI ENGINEERING COLLEGE MORBI BRANCH:MECHANICAL ENGINEERING SEMESTER:3 YEAR:2014-15 GUIDED BY: I.B.SHAH PREPARE BY: Saravadiya Deep Detroja Viral Dhanani Kalpesh (130310119013) (130310119014) (130310119015) Coriolis Components Of Acceleration Coriolis Effect 1. In physics, the Coriolis effect is a deflection of moving objects when the motion is described relative to a rotation referance frame 2. In a reference frame with clockwise rotation, the deflection is to the left of the motion of the object; in one with counter-clockwise rotation, the deflection is to the right. 3. . Although recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist gaspard-gustav Coriolis, in connection with the theory of Water wheels. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology Formula • The vector formula for the magnitude and direction of the Coriolis acceleration is ac=-2ῼ * v 2. where (here and below) is the acceleration of the particle in the rotating system, is the velocity of the particle in the rotating system, and Ω is the angular velocity vector which has magnitude equal to the rotation rate ω and is directed along the axis of rotation of the rotating reference frame, and the × symbol represents the cross product operator. • The equation may be multiplied by the mass of the relevant object to produce the Coriolis force: Fc=-2m ῼ * v See fictitious force for a derivation. Causes • The Coriolis effect exists only when one uses a rotating reference frame. In the rotating frame it behaves exactly like a real force. However, Coriolis force is a consequence of inertia and is not attributable to an identifiable originating body, as is the case for electromagnetic or nuclear forces • In meteorology, a rotating frame (the Earth) with its Coriolis force proves a more natural framework for explanation of air movements than a non-rotating, inertial frame without Coriolis forces. In long-range gunnery, sight corrections for the Earth's rotation are based upon Coriolis force. These examples are described in more detail below. Causes • Suppose the roundabout spins counter-clockwise when viewed from above. From the thrower's perspective, the deflection is to the right.[ From the non-thrower's perspective, deflection is to left. For a mathematical formulation see Mathematical derivation of fictitious forces. • An observer in a rotating frame, such as an astronaut in a rotating space station, very probably will find the interpretation of everyday life in terms of the Coriolis force accords more simply with intuition and experience than a cerebral reinterpretation of events from an inertial standpoint. • The apparent acceleration is proportional to the angular velocity of the reference frame (the rate at which the coordinate axes change direction), and to the component of velocity of the object in a plane perpendicular to the axis of rotation. This gives a term -ῼ*v The minus sign arises from the traditional definition of the cross product and from the sign convention for angular velocity vectors. Rotating Sphere Consider a location with latitude φ on a sphere that is rotating around the north-south axis. A local coordinate system is set up with the x axis horizontally due east, the y axis horizontally due north and the z axis vertically upwards. The rotation vector, velocity of movement and Coriolis acceleration expressed in this local coordinate system (listing components in the order east (e), north (n) and upward (u)) are: Distance Star • The apparent motion of a distant star as seen from Earth is dominated by the Coriolis and centrifugal forces. Consider such a star (with mass m) located at position r, with declination δ, so Ω · r = |r| Ω sin(δ), where Ω is the Earth's rotation vector. The star is observed to rotate about the Earth's axis with a period of one sidereal day in the opposite direction to that of the Earth's rotation, making its velocity v = –Ω × r. The fictitious force, consisting of Coriolis and centrifugal forces, is: Meteorology • Perhaps the most important impact of the Coriolis effect is in the large-scale dynamics of the oceans and the atmosphere. In meteorology and oceanography, it is convenient to postulate a rotating frame of reference wherein the Earth is stationary. In accommodation of that provisional postulation, the centrifugal and Coriolis forces are introduced. Their relative importance is determined by the applicable Rossby numbers. Tornadoes have high Rossby numbers, so, while tornado-associated centrifugal forces are quite substantial, Coriolis forces associated with tornadoes are for practical purposes negligible.[22] Eotvos Effect • The practical impact of the "Coriolis effect" is mostly caused by the horizontal acceleration component produced by horizontal motion. • There are other components of the Coriolis effect. Eastward-traveling objects will be deflected upwards , while westward-traveling objects will be deflected downwards . This is known as the Eötvös effect. This aspect of the Coriolis effect is greatest near the equator. The force produced by this effect is similar to the horizontal component, but the much larger vertical forces due to gravity and pressure mean that it is generally unimportant dynamically. • In addition, objects traveling upwards or downwards will be deflected to the west or east respectively. This effect is also the greatest near the equator. Since vertical movement is usually of limited extent and duration, the size of the effect is smaller and requires precise instruments to detect. Coriolis effects in other areas • Coriolis flow meter • Molecular physics • Gyroscopic precession • Insect flight Insect flight • Flies (Diptera) and moths (Lepidoptera) utilize the Coriolis effect when flying: their halteres, or antennae in the case of moths, oscillate rapidly and are used as vibrational gyroscopes.See Coriolis effect in insect stability. In this context, the Coriolis effect has nothing to do with the rotation of the Earth. Gyroscopic precession • When an external torque is applied to a spinning gyroscope along an axis that is at right angles to the spin axis, the rim velocity that is associated with the spin becomes radially directed in relation to the external torque axis. This causes a Coriolis force to act on the rim in such a way as to tilt the gyroscope at right angles to the direction that the external torque would have tilted it. This tendency has the effect of keeping spinning bodies stably aligned in space. Coriolis flow meter • A practical application of the Coriolis effect is the mass flow meter, an instrument that measures the mass flow rate and density of a fluid flowing through a tube. The operating principle involves inducing a vibration of the tube through which the fluid passes. The vibration, though it is not completely circular, provides the rotating reference frame which gives rise to the Coriolis effect. While specific methods vary according to the design of the flow meter, sensors monitor and analyze changes in frequency, phase shift, and amplitude of the vibrating flow tubes. The changes observed represent the mass flow rate and density of the fluid. Molecular physics • In polyatomic molecules, the molecule motion can be described by a rigid body rotation and internal vibration of atoms about their equilibrium position. As a result of the vibrations of the atoms, the atoms are in motion relative to the rotating coordinate system of the molecule. Coriolis effects will therefore be present and will cause the atoms to move in a direction perpendicular to the original oscillations. This leads to a mixing in molecular spectra between the rotational and vibrational levels from which Coriolis coupling constants can be determined. References • http://en.wikipedia.org/wiki/Coriolis_effect#F ormula